" Solving this requires a number of hashing operations. How many depends on how many coins have been minded previously so it’s an increasing level of difficulty."
Actually no, the difficulty to generate coins is based on the computing power of the network and adjusted every two weeks to keep the flow of coins constant. So the more mining rigs running the harder it gets.
There is a separate adjustment made every couple of years that halves the rate of coins produced, but this is purely based on time.